In 2021, the Nobel Committee did something unusual: it gave half a Physics prize to climate science and the other half to the mathematics of broken glass. What connects them — and what connects all three laureates — is a single, radical insight: that you cannot understand a complex system by ignoring its noise. You have to make the noise the subject.
The Men Who Built the Climate in a Computer
Syukuro Manabe was born in rural Japan in 1931, trained as a meteorologist, and in 1959 found himself at a small US government laboratory in Princeton that had been quietly working on a strange and ambitious project: simulating the entire atmosphere on a computer. He would spend the next four decades there, asking a deceptively simple question — if you pour more carbon dioxide into the atmosphere, how much warmer does the planet get?
Klaus Hasselmann, meanwhile, grew up in Hamburg and London, became fascinated by the physics of ocean waves, and arrived at the same question from a completely different direction. Where Manabe was a builder of models, Hasselmann was a theorist of noise. He wanted to understand why the climate varies in the first place — why the ocean has long memories, why weather seems random but climate seems predictable — and whether you could ever prove that humans were responsible for the warming trend already appearing in observations.
Together, their work forms the scientific backbone of everything we now know about human-caused climate change. Manabe's numbers — how much warming to expect from a doubling of CO₂ — have stood up for nearly sixty years. Hasselmann's statistical framework is the reason the IPCC could declare, in 2013, that it is "extremely likely" that human influence is the dominant cause of observed warming since the mid-twentieth century. That sentence rests entirely on mathematics Hasselmann invented.
Why the Atmosphere Is Hard, and What Manabe Did About It
The problem with simulating Earth's climate is that it involves everything at once. The sun heats the surface; the surface heats the atmosphere; water evaporates, rises, and condenses, releasing more heat; clouds form and reflect sunlight back to space; ocean currents redistribute warmth across hemispheres. Every part of the system talks to every other part, across timescales ranging from seconds to millennia.
Before Manabe, physicists had been trying to model the greenhouse effect since the 1890s, when the Swedish chemist Svante Arrhenius first calculated that doubling atmospheric CO₂ might warm the planet by about 6°C. But Arrhenius was working by hand, with crude spectral data, and his atmosphere was a single, isothermal layer. What was needed was a proper column model — a vertical slice of the atmosphere, from the ground to the stratosphere, with the right temperatures, the right humidity, and the right physics of how infrared radiation is absorbed and emitted at each level.
Manabe's great insight was to include the water vapour feedback correctly. The most potent greenhouse gas in the atmosphere is not CO₂ but water vapour — and its distribution is controlled by the temperature, not by us. As the planet warms, the atmosphere holds more water vapour, which warms it further. Manabe realised you had to fix the relative humidity (the fraction of saturation) rather than the absolute humidity, which naturally captures this feedback. It seems technical. But it was the difference between getting the answer right and getting it completely wrong.
In their landmark 1967 paper, Manabe and Wetherald built a one-dimensional atmospheric column with realistic relative humidity and ran it forward to equilibrium. They then doubled the CO₂ concentration and ran it again. The result: 2.3°C of warming per doubling of CO₂ — a number they called climate sensitivity.
By 1975, Manabe had extended this to a full three-dimensional global model. Doubling CO₂ from 300 to 600 ppm produced 2.93°C of warming. Modern climate models, with vastly more computing power and six more decades of observational data, give a range of 2.5–4°C. Manabe's first attempt landed square in the middle.
Weather Is the Noise. Climate Is the Signal. Can You Tell Them Apart?
Even as Manabe was building his models, a harder problem was waiting. Climate models can tell you what should happen if you double CO₂. But the real atmosphere is a cacophony — storms, El Niño events, volcanic eruptions, solar cycles. The warming signal, if it exists, is buried in all this noise. How do you find it? How do you ever prove that humans did it?
Hasselmann's first contribution was to explain where the noise comes from. In a beautiful 1976 paper, he showed that the slow, long-term variability of the ocean — the decades-long swings in sea surface temperature that seem so mysterious — is simply the ocean integrating the fast, random fluctuations of the atmosphere above it. Weather is the noise; the ocean acts as a kind of low-pass filter, averaging it into something that looks like a long, slow signal. He called this "stochastic climate models," and the analogy was direct: it is exactly how a pollen grain in water (Brownian motion) accumulates random kicks from water molecules into a long, wandering path.
His second contribution was even more consequential: the fingerprinting method. He realised that different causes of climate change leave different spatial patterns in the observations — the three-dimensional signature of greenhouse gas warming looks different from the signature of solar variability, or of volcanic eruptions. If you could characterise these fingerprints precisely and then search the observational record for them, you could not only detect change but attribute it to a specific cause. The logic was elegant: don't look for the signal where it's strongest, look for it where the noise is weakest.
Don't look for a needle in a tiny corner of a haystack. Search the entire haystack simultaneously — because you already know the shape of the needle.
— Paraphrase of Hasselmann's approach, as described by climate scientist Ben Santer and colleaguesGiorgio Parisi and the Problem That Was Eating Physics
Giorgio Parisi was born in Rome in 1948, and by the mid-1970s he had already published significant work in quantum field theory and particle physics. Then he turned his attention to something seemingly humbler: a peculiar class of materials called spin glasses. It would take him nearly a decade to crack them. The solution, when it came, turned out to be one of the most original mathematical structures in the history of physics.
A spin glass is a disordered magnet — a metal alloy in which a small number of magnetic atoms are scattered at random through a non-magnetic host. Each magnetic atom, or "spin," wants to align with its neighbours. But the interactions between spins are also random: some pairs want to align in the same direction (ferromagnetic), while others prefer to be opposite (antiferromagnetic). The result is a system where no single arrangement can satisfy all the constraints at once. Physicists call this frustration.
The simplest illustration: imagine three spins arranged in a triangle, with each pair wanting to be antiparallel. Flip them however you like — you can satisfy any two constraints, but the third is always violated. Scale this up to billions of atoms, with random interactions varying across the whole material, and you have a system that can never fully relax. It gets stuck in one of a vast number of long-lived metastable states — local energy minima that aren't the true ground state — and it sits there, effectively, forever. This is the glass-like behaviour that gives spin glasses their name.
Place three magnets at the corners of a triangle. Each one wants its neighbour to point the opposite way. Call the two options ↑ and ↓. If A=↑ and B=↓, they're happy. If B=↓, then C wants ↑. But then C and A are both ↑ — and they wanted to be opposite. There is no configuration that makes everyone happy. This is frustration in its purest form. Now imagine not three spins but ten billion, with randomly varying preferences — and you have a spin glass.
Replica Symmetry Breaking, or: How Many Ways Can a Glass Be Stuck?
By the mid-1970s, physicists had a mathematical model for spin glasses, developed by Edwards and Anderson, and a mean-field version developed by Sherrington and Kirkpatrick. The mean-field model was tractable — it could, in principle, be solved exactly. There was just one problem: when they tried to solve it, the entropy of the system came out negative at low temperatures. Negative entropy is physically impossible. Something was deeply wrong.
The culprit, it turned out, was an assumption so natural it had barely been noticed: that all the replicas of the system — all the different copies you might make of it under identical conditions — were equivalent to one another. This assumption is called replica symmetry. It works for ordinary magnets, where the system, if cooled, falls into one of two ordered states (all spins up, or all spins down) and all copies made at the same temperature will be in the same state. But for spin glasses, Parisi showed, it is catastrophically wrong.
His insight was that a spin glass doesn't have two ordered states. It doesn't have ten. It has infinitely many — a whole hierarchy of distinct, long-lived configurations, nested inside each other in a precise mathematical structure. When you cool two replicas of a spin glass to the same temperature, they won't necessarily end up in the same state. They might end up in states that are very similar, or moderately similar, or barely related at all. Parisi introduced an order parameter — a function rather than a number — to describe the distribution of possible overlaps between replicas. This was replica symmetry breaking.
Physicists call these distinct stable configurations multiple equilibria: states a system can occupy indefinitely, none more correct than another, with no guaranteed path between them. In an ordinary magnet, there are exactly two. In a spin glass, there are infinitely many, arranged in a nested hierarchy. The concept turns out to be one of the most portable in all of science — it reappears wherever a system has competing constraints and no single preferred resolution. The same structure surfaces in economics, where markets can settle into different coordination outcomes depending on history; in ecology, where ecosystems can be stable at very different population levels; and, as we will see in the next lecture in this series, in game-theoretic models of how agents reach agreement. Multiple equilibria, once you know to look for them, are everywhere.
- Two stable ground states (↑ all or ↓ all)
- Symmetry broken once, cleanly
- All replicas end up the same
- Energy landscape: a simple valley
- Described by a single number (order parameter)
- Infinitely many metastable states
- Symmetry broken in an infinite hierarchy
- Replicas can end up in very different states
- Energy landscape: a mountainous corrugated terrain
- Described by a whole function (Parisi's order parameter)
From Broken Magnets to Neural Networks, Optimisation, and Light Itself
A mathematical structure invented to fix a broken model of a disordered magnet might seem like a curiosity — important to specialists, invisible to everyone else. In fact, replica symmetry breaking turned out to be one of the most generative ideas in twentieth-century physics, spreading into fields that had nothing to do with magnetism and illuminating problems that had seemed entirely unrelated.
The first surprising connection was to neural networks. In 1982, physicist John Hopfield described a model of associative memory — a network of simple units that could store patterns and retrieve them when given a partial cue. Parisi and his collaborators showed that the multiple memories stored in a Hopfield network correspond precisely to the multiple metastable states of a spin glass. The energy landscape of a trained neural network is a corrugated terrain; the memories are the valleys. This was not a metaphor. It was exact mathematics — the same mathematics Geoffrey Hinton (Physics Nobel 2024) would later use to build Boltzmann machines and, ultimately, the foundations of modern deep learning.
Beyond neural networks, the replica framework illuminated the travelling salesman problem and other combinatorial optimisation challenges — explaining precisely why some problems are easy to solve and others are effectively impossible, and why randomised algorithms like simulated annealing (itself inspired by spin glass physics) work as well as they do. It provided the modern theory of structural glasses and the mechanics of jamming, explaining why a pile of sand stops moving when you compress it. Most remarkably of all, experimental evidence for replica symmetry breaking has now been found in random lasers — exotic optical systems where stimulated emission happens in a disordered medium — where the pump power plays the role of inverse temperature and the emission spectra of individual shots are the replicas.
Parisi proved his solution to the spin glass problem in the late 1970s. It was mathematically audacious, physically surprising, and almost immediately influential. But it was not rigorously proven — not in the sense that mathematicians demand. The replica trick (taking the logarithm of a partition function by writing it as the limit of n copies as n approaches zero) is a formal sleight of hand whose justification was, for decades, more intuitive than rigorous.
The full mathematical proof that Parisi's solution is correct for the Sherrington–Kirkpatrick model came in 2006 — from mathematician Michel Talagrand, working in the theory of probability, nearly thirty years after Parisi first wrote it down. Physicists had been using it, confidently and correctly, the whole time. It is one of the most striking examples in modern science of physical intuition running so far ahead of mathematical proof that the proof had to sprint to catch up.
What Disorder Teaches Us About Everything
The Nobel Committee's description of this prize — "for groundbreaking contributions to our understanding of complex physical systems" — sounds like the sort of politely vague language committees use when a prize covers too much ground. But there is a genuine unity here, and it is worth sitting with it.
Manabe showed that climate sensitivity — the key number governing how much warming we should expect — could be calculated from first principles, and his number has held up. Hasselmann showed that the noise in the climate system is not an obstacle to prediction but the very thing that enables attribution: by characterising natural variability precisely, you can identify the human fingerprint against it. Parisi showed that a system with no single ground state, no one preferred configuration, no clean ordered phase, is not a system that defeats physics — it is a system whose disorder has its own deep mathematical structure, its own order parameter, its own exact solution.
Together they make a single argument: complexity is not intractable. Disorder is not the absence of structure. Noise is not the enemy of signal. These are lessons that reach far beyond physics — into epidemiology, economics, ecology, and the design of machine learning systems. They are also, in the case of Manabe and Hasselmann's work, lessons with an urgent practical dimension. We do not have the luxury of waiting for perfect certainty about a changing climate. What these laureates gave us is something better than certainty: a rigorous account of what we know, how well we know it, and precisely how confident we should be.
The physicist Richard Feynman is quoted in the scientific background document to this prize: he believed, it is said, "in the primacy of doubt — not as a blemish on our ability to know, but as the essence of knowing." That is a good description of what Manabe, Hasselmann, and Parisi each achieved. They took the doubt seriously, gave it precise mathematical form, and found that in doing so they had also found the truth.
Parisi, Manabe & Hasselmann in Stockholm, 2021
Prize Lectures delivered December 8, 2021, at Aula Magna, Stockholm University.
Individual lecture pages: Parisi · Manabe · Hasselmann
Read the Original
The scientific background document is unusually rich — written for physicists but covering the full sweep of climate science and statistical mechanics from first principles. The sections on Hasselmann's stochastic framework and Parisi's replica symmetry breaking are worth reading slowly.
Go Deeper
- In a Flight of Starlings by Giorgio Parisi (2023) — Parisi's own short, beautifully written account of how science works, using his career as a thread; accessible and surprisingly personal for a theoretical physicist.
- The Warming Papers ed. Archer & Pierrehumbert (2011) — A curated collection of the foundational papers in climate science, including Manabe and Wetherald's 1967 paper, with editorial commentary that makes the history legible.
- Spin Glass Theory and Beyond by Mézard, Parisi & Virasoro (1987) — The technical bible of the field, co-authored by Parisi; not for the casual reader, but the introduction is a remarkably clear statement of what the problem is and why it matters.
- The Climate Crisis by David Archer & Stefan Rahmstorf (2010) — A clear, scientifically rigorous introduction to climate science for non-specialists, grounded in the kind of physics Manabe and Hasselmann pioneered.